Physical and Mathematical Modeling of Earth and Environment Processes

In the geological past, there was a continental formation in the place of the Tyrrhenian-Ligurian basin, that included Sicily, Sardinia, Corsica, and the Apennines in the southwest of the Italian peninsula. The stretching processes led to rifting, passing into diffuse spreading with the fragmentation of this formation. Calculation of Eulerian poles and rotation angles in the context of complex geological and geophysical interpretation of bottom geomorphology allowed to restore the spatial position of the axes of the initial split of the continental formation and to describe the kinematics of the microplates of analyzed region.

The effect of slopes created by long waves on the resonance backscattering of microwave radio waves analyzed. The analysis is carried out within the framework of the Gaussian model of slopes distribution. The polarization ratio increases by approximately 10% as the wind speed increases up to 5 m/s if the sounding is performed along the direction of wind. If the sensing is accomplished across the direction of wind, as the wind speed tends to 5 m/s the polarization ratio increases to approximately 6%. The effect of the presence of long waves weakly depends on the incidence angle.

This paper presents a review of existing methods and sorbents for elimination of hydrocarbons spills from the water surface. The characteristics and operating principles of the existing devices are described. Experimental study of the sorption capacity of various substances and the usage of these substances for the elimination of hydrocarbon contamination of water surface are made. The measurements have shown that raw sheep’s wool absorbs at least 6 times its weight in oil and other hydrocarbons. The sample of the device for liquidation of hydrocarbons spills on the surface of water is designed. The designed device can be used to eliminate surface spills of various hydrocarbons on water objects in two modes: from a board of surface craft and from waterfront.

The hydrodynamic regime of the seas and oceans plays an important role for mankind’s economic activity and the formation of the Earth’s climate. Internal waves are observed everywhere in the ocean and permeate all of its thickness, and therefore are an important component of hydrodynamics of water masses. Internal waves have a great importance for solving a number of applied problems, such as underwater navigation, transportation and extraction of hydrocarbons, hydraulic engineering, fishing, as well as for biology, sedimentation and optics of the ocean. The purpose of the investigation is to study the influence of various hydrological conditions of the northern and southern seas of Russia on the formation of modes of internal waves and their comparison with ocean conditions by the example of the hydrological situation of the central Atlantic.

The analysis of critically stressed fractures’ relationship to elastic moduli of the rock is carried out. Series of triaxial loading tests were performed for rock samples. The behavior of differential stress vs. volumetric strain curve in the vicinity of elasticity limit of the rock is particularly analyzed. It is revealed that the slope of this curve changes considerably when the principal stresses exceed the specific values determined by the criterion of critically stressed fractures appearance. Thus the relationship between fracture initiation Griffith criteria and critical stress state of fractures in the medium is established. It is shown that it is possible to define a specific elastic modulus which is influenced by the fraction of critically stressed fractures in the rock. This modulus may be used to solve the inverse problem of stress state estimation from independent observations related to fractures. Moreover, a formalized approach for estimation of the parameters of rock failure criterion from a cyclic loading test is proposed.

In the current work, depth-sensing indentation tests were applied at different coals microcomponents in order to characterize their mechanical properties. To this end, three coals were chosen differing by their rank and properties. Thin transparent films of such coals were prepared as samples in order to use transmitted light microscopy to achieve exact positioning of indent probe in the zone occupied by specific coal microcomponent. Experimental procedures allowed obtaining load-displacement curves at different microcomponents. These curves revealed differences between microcomponent vitrinite behavior among coals of different types. Measured values of elastic moduli and hardness also proved that they variate with coal rank. It was concluded that matrix of coals (vitrinite microcomponent) transforms its mechanical properties with rank, whereas the inclusions properties do not change as significantly.

Method of the adjoint equations, estimation method and variational algorithm of the input parameters identification of the passive admixture transport model is considered in that work. Modification of the variational algorithm of the measurements data assimilation, allows saving the calculation resources under the algorithms numerical realization considerably. Problem of the contamination point source power estimation on the base of the evaluation method and working out the obtained estimations is solved. The numerical experiments for estimation the concentration fields according to the initial data and solving the corresponding adjoint problem are conducted. Variation algorithm of the initial pollution spot identification is realized. Possibility to use assimilation variational methods and measurements data filtration for the wide range of problems connected with investigated basin ecological state was shown in the present work. Modified scheme for realization of the variational algorithm identification of the model input parameters is suggested. Conditions, under which the suggested algorithm has advantages over the standard approach, were obtained. The conducted numerical experiments have shown the proven work of the identification algorithm of the contamination source parameters applying the passive admixture transport model in the Azov Sea. Good converging of the iteration process and accuracy of the concentration field initial distribution determination was obtained for the variational algorithm of the passive contaminant concentration initial field identification.

The article describes physical mechanisms accounting for interannual variability of horizontal heat advection in the upper mixed layer (UML) in the North Atlantic in January and July. The data from ocean reanalyses ORA-S3, GFDL and GODAS over 1980–2011 are used for this analysis. The relative contribution of currents’ intensity, horizontal temperature gradients and their mutual influence into interannual variations of the advective heat transport in the UML is examined. In the most part of the North Atlantic basin, the variations of currents’ intensity are crucial factor accounting for the UML anomalies. The interannual heat advection anomalies in the Guiana current and the Gulf Stream vicinity (before veering off the continental slope) in January and July are caused by temperature gradients variations. In general, the influence of horizontal temperature gradient anomalies transported by abnormal currents in the North Atlantic is small.

In the article, it is considered a modification of an integral model of unsteady turbulent jet with a presence of pressure force. Stationary solutions of the presented model is compared with well-known analytical results of classical models. It is shown that the inclusion of pressure forces changes dynamic parameters of a jet by about 15%. An analytical solution of a steady forced buoyant jet that corresponds to a volcanic outburst is deduced. An analytical solution for the spontaneous jet of convective surface layer is presented. The simplest model of an ensemble of the buoyant jets of convective surface layer is built. A hydrodynamic formation mechanism of vertical profiles of the turbulent diffusivity and the turbulent statistical moments of the atmospheric surface layer related to the ascent of the jets’ system, is formulated.

Over the last few years interest in the multidisciplinary approach to modeling and evaluating processes associated with the development of oil and gas fields has incredibly increased. The authors of the article studied the effects of rock on the filtration-capacitive, physical and mechanical properties of the rock. The coefficients of porosity, permeability and cementation factor change were estimated taking into account water saturation of rock samples.

The research of Earth’s physical fields and their variations is particularly important to establish causes and mechanisms of changes in the environment and in the climate. The results of the analysis of instrumental observation concerning the variations in electric and magnetic fields, as well as acoustic vibrations in the near-surface Earth zone are considered in relation to the variations of meteorological parameters. We used the results of synchronous observations concerning physical fields carried out in the period of 2011–2014 in conductions of Geophysical observatory “Mikhnevo” of Institute of Geosphere Dynamics of Russian Academy of Science (IDG RAS) (Russia, Moscow region, settlement Mikhnevo; 54.959º N, 37.766º E). Synchronism of the variations of mentioned geophysical fields and change in atmospheric parameters has been determined, and for the first time not only synchronous, but advanced manifestations of geomagnetic field perturbations are shown, we introduce a new parameter - “reverse” magnetic tipper, variations of which due to atmospheric disturbances are more strongly marked in comparison with the variations of magnetic tipper.

In the Boussinesq approximation, free inertia-gravity internal waves are considered in a two-dimensional vertically non-uniform flow. In the linear approximation was find vertical distribution of the amplitude of the vertical velocity and the dispersion relation. The boundary-value problem for internal waves has complex coefficients when the flow velocity component, transverse to the wave propagation direction depends on the vertical coordinate. Therefore, the eigenfunction and frequency of the wave are complex (it is shown that there is a weak damping of the wave). Vertical wave mass fluxes are nonzero. The vertical component of the Stokes drift velocity also differs from zero and contributes to the wave transport. A non-oscillating on a time scale of the wave correction to the average density, which is interpreted as an irreversible vertical fine structure generated by a wave, is determined on the second order of amplitude.

An attempt is made to apply the modern methods of surface wave simulation developed for oceanic conditions to the modeling of waves in medium-size inland reservoirs (10–100 km). The results of field measurements of wind speed and waves are described, and on their basis the parameterization $$ C_{D} \left( {U_{10} } \right) $$CDU10 is proposed. WAVEWATCH III spectral wave model was adapted to the conditions of a medium-size inland reservoir. The simulated data are compared with the field data. The use of the new parameterization $$ C_{D} \left( {U_{10} } \right) $$CDU10 allowed reducing the values of the wind wave growth rate that improved consistency in data from the field experiment and numerical modeling concerning the height of significant waves. Further steps towards improving the quality of prediction of the adapted WAVEWATCH III model are discussed.

The article describes a manifestation of Atlantic multidecadal oscillation (AMO) in the variability of hydro-thermodynamic characteristics and ocean surface heat fluxes in North Atlantic. It is shown that multidecadal changes in the upper mixed layer temperature and mixed layer depth, as well as sea surface height (SSH), are statistically significant and show physically consistent changes. Convective mixing of waters at high latitudes is stronger for negative AMO phase with an exception the case of Great Salinity Anomaly. Large-scale fluctuations in SSH are most pronounced in the eastern part of North Atlantic. Multidecadal changes in the net surface heat fluxes and horizontal heat advection are coherent. The increase (decrease) of horizontal heat advection in the negative (positive) AMO phase leads to an increase (decrease) of the ocean heat release to the atmosphere. Multidecadal variability of the horizontal heat advection is due to changes in the dynamics of currents, rather than temperature gradients.

Hydrophysical fields, continuous in time and space, were reconstructed in the coastal region of the Black Sea (a western coast of the Crimea and a north-western shelf of the Black sea) on the basis of the three-dimensional nonlinear hydrodynamic model and the observational data of temperature and salinity on the research vessel “Experiment” from 16 to 22 of September, 2007. A sequential optimal interpolation of observational data of temperature and salinity was used as an assimilation procedure. A real atmospheric forcing and a high resolution (horizontal grid ~1.6 × 1.6 km and 30 vertical layers from 1 m to 1300 m) were used in the calculation. Mesoscale features of currents and thermohaline fields in the coastal zone of the Black Sea were investigated, the coastal upwelling in the Kalamitsky Bay was reconstructed, registered in satellite observations. The influence of the assimilation of observational data on the accuracy of the calculated fields of temperature and salinity was estimated.

Physical processes of heat and mass vertical transfer in natural stratified basins depend mostly on the intensity of quasi-inertial internal waves breaking, which, in turn, is determined by the intensity of the wave source and local stratification in the basin. There are many research works including estimations of the dependence of the vertical turbulent diffusion coefficient K on the buoyancy frequency N (stratification). In this paper, on the base of a semiempirical model using the analysis of the pulsation data obtained at probing in the lower stratified part of the Black Sea active layer, the dependence of the coefficient of vertical turbulent diffusion K on the buoyancy frequency N is estimated. The measurements were carried out in the deep area of the basin. The measurement data were collected using a high-resolution probe-turbulimeter “Sigma-1”. A similar dependence for this layer was built based on a 1.5D model of the vertical exchange in the Black Sea deep region. Previously, the same results were obtained in the upper “strongly” stratified and the lower “weakly” stratified layers in the main pycnocline of the investigated basin. The joint analysis of three pairs of power dependencies $$ K \cong AN^{\alpha } $$K≅ANα m2s−1 from different stratified layers showed that the exponents α in each pair were very close to each other, while the estimated (semi-empirical) coefficients A in each pair turned out to be much higher than the pattern coefficients.

A model of oscillations of Earth’s poles is constructed on the basis of the analysis of the gravitational torques from Sun and Moon. The model reflects physical processes and does not imply using curve fitting techniques, based, for example, on the polynomial approximation. Within the framework of this model, the Chandler frequency is interpreted as the fundamental frequency of oscillations of the mechanical system and the annual frequency as the frequency of the excitation force. A fine mechanism of excitation of the oscillations based on the combination of natural and forced frequencies is revealed. The model has only six parameters that can be identified by applying the least squares technique to the experimental data of the International Earth Rotation and Reference Systems Service. The prediction provided by the proposed model has high degree of accuracy for an interval of several years.

It is shown that upon a metal explosion of the wire between the electrodes caused by a pulsed arc discharge inside a dielectric ring on the cathode melts with hole formation. Solidification of the cathode metal is accompanied by the appearance of rings on the cathode surface, which may indicate the presence of wave motion. Analogous ring structures of a much larger size can also be found on the Earth surface. Their occurrence may be due to a meteorite explosion in the Earth atmosphere followed by generation of huge electric fields and a breakdown between the meteorite substance and the Earth.

When controlling the Apparatus Function (AF), the size of definition domain of the AF O and the sampling step and conditionality of the AF must be chosen so that its inverse function $$ {\text{pR}} = {\text{pO}}^{ - 1} $$pR=pO-1 obtains a minimum norm. The compensation of the AF O distortions in the measured images is realized point-by-point (without using the Fourier Transform in convolution). The computer of the device uses the resolving function pR, selected by the controlling procedure, for achieving super-resolution in images. Such controlled super-resolution is demonstrated on the Martian images.

In this paper the spatial pattern of vortex flow around the rotating disk studied experimentally. The disk is mounted in a continuously stratified fluid. The phenomenon of breaking the annular flow near the disk edges to a regular sequence of vortex loops is found. The governing parameters are found and the range of their values is determined. Observations have been made both for strongly stratified and for weakly stratified media. The influence of stratification on the evolution of the current is determined.

Based on a comparison of Cox-Munk and Bréon-Henriot empirical models of the sea-surface slopes probability density that are more close to the results of satellite observations as compared to other empirical models, an estimate of their practical error for winds equal to 1, 3, 7, 14 m/s is presented. Also, values of the discrepancy between the Cox-Munk model and that frequently used simplified forms are calculated, along with the discrepancy between the Cox-Munk model and its modification that, unlike the original one, is non-negative for all possible slopes and wind speeds. The physical causes of the discrepancy between the Cox-Munk and Bréon-Henriot models typical for small and large wind speeds are considered. It is shown that to reduce the systematic errors of empirical models of the sea-surface slopes probability density, it is necessary to study and take into account the effect of thermal stability of the marine boundary layer on their parameters.

In this paper we consider a self-consistent mathematical model and numerical simulation techniques which are supposed to be suitable to analyze behavior of the impermeable porous media with isolated pores filled with chemically active multiphase multicomponent substance under thermal loads. The porous matrix is described by linear thermomechanical equations. The substance in pores is described by lumped model which includes chemical (pseudo) components mass conservation equations and energy conservation equation for the mixture. Amount of components can change due to chemical reactions induced by heating of the media. Lumped energy balance equations account for matrix/pores heat transfer and heat produced by chemical reactions. Composition of phases is governed by phase equilibrium conditions with an arbitrary number of components and four phases (solid, liquid hydrocarbon, gas and liquid water phases). The two groups of equations (for the matrix and for the pores) are coupled by suitable interface conditions at the “reservoir”/“pore” interfaces.The purpose of the model is a validation of the basic mechanisms of the formation of connected porosity and permeability in the initially impermeable heavy hydrocarbon reservoirs treated by the modern thermal recovery techniques such as, e.g., in citu combustion.Preliminary numerical results are presented for synthetic but realistic test case.

We consider the problem of the development of two-dimensional vortex with initial vorticity in the peripheral ring area of the circularly rotating incompressible viscous fluid. As a mechanism for the generation of vortex motion, we propose the model of plain circular rotation of incompressible viscous fluid with initial perturbation localized at the peripheral ring zone with rate shift. Based on the analytical solution axisymmetric nonstationary equation of plain evolution of vortex in viscous fluid we obtained the resulting integral for the vorticity in the whole area of rotating fluid. This allowed us to study the dynamic characteristics of oceanic vortex formations and the time duration of the vortex motion conservation in a viscous liquid. The presented calculations given here show that the process of vorticity generation is characterized by the complex of interacting movements from the main vortex in the center of the rotating system and from the peripheral secondary perturbations. Vortex formation occurs in such direction that the central vorticity intensifies due to the secondary perturbations, as a result forming two areas – vortex and potential – of the rotating system. The obtained calculation results for the vorticity generation time in rings forming at the meanders of Gulf Stream jets, when compared to the observational data, show that lifespan of rings of different scales distributes rather variously according to their sizes and viscosity, the value of which correspond to turbulent regimes of jet streams. We discuss the prospect of its possible applications for predictive analysis of the development dynamics of large-scale ocean eddies.

This article includes an issue of applying a reservoir proxy model as a component part for geo-technological model of gas fields and underground gas storages. Authors have proposed an algorithm of applying the created proxy model into intelligent management system for gas fields and UGS. The task of proxy model creating is considered by the example of an underground gas storage “X” (the name of the object is encrypted commercial confidentiality reasons). All characteristics of the object “X” and the data on its actual operation mode, whereon model adaptation was performed, are given in the article. Authors have presented a detailed mathematical description of reservoir proxy model and considered the process of its creation, adaptation and integration into a geo-technological model complex of an object. Also, the limits of applicability of this method was determined. A Fully Functional Hydrodynamic (FFH) model of the “X” object was created in the commercial simulator «Schlumberger Eclipse» in order to assess the correctness of the reservoir proxy model, and a detailed comparison of the actual data and model calculations was conducted. In addition, the issue of using hydrodynamic models as a core of intelligent management system for reservoir development was considered in detail. The conclusions made by authors tell about the necessary of computing capacities, both for operation of the proxy model and the FFH model based on the commercial simulator. As a result of the research, conclusions about the applicability of the reservoir proxy model as an integral part of geo-technological model of gas fields and UGS were made.

Different rock material dynamic laboratory tests have been analyzed with the help of incubation time criteria approach. As a result of made calculations incubation times for such rocks like granite, marble, limestone, sandstone and traverline have been estimated. This parameter according to criteria theory rule material behavior under high rate loadings. Effects of effective porosity and anisotropy on incubation time value have been considered. Experiments under high rate loadings with different saturation and temperatures have been demonstrated influence of physical conditions changes on incubation time parameter.

The article discusses methodological contradictions and their effects that occur when interpreting the results of researches of relative permeability by the method of non-stationary displacement. For the case of mutual displacement of liquids with equal viscosities on the simplest structural model of a porous medium, an important aspect is shown: the discrepancy between the functions of the average filtration rate and the flow of the displacing phase in the exit section of the sample from the saturation of the cross section. This aspect changes the concept of the nature of the processes of two-phase displacement of liquids in an inhomogeneous porous medium.

In this paper we present the results of the laboratory experiment aimed at the research of the hydraulic fracture propagation rate. The laboratory experiment was carried out according to similarity criteria. The fracture growth rate was determined by one direct method and two indirect methods. The direct method was based on registering the formation of the fracture by conductive strips. The first indirect method was based on the variations of the pressure in the well. The second one was based on a numerical solution of the problem of hydraulic fracture propagation.

Based on the results of a study of the magnetic properties of basalt samples dredged from the Red Sea rift zone at a latitude of 18° N, and of geomagnetic field paleointensity determination by Thellier–Coe method, it was concluded that the studied basalts are related to three different stages of crust formation in this region. It is determined that the geomagnetic field paleointensity at the time of formation of the studied basalts samples was 1.1–1.9 times higher than current geomagnetic field intensity in this region. Obtained results indicate that the geomagnetic field intensity in this region have been decreasing in the last 100 thousand years.

We report on the experimental studies of the influence of two different types of hydrodynamic perturbations on the characteristics of laser radiation scattering in the near-water aerosol layer. Laboratory experiment was carried out in a tank with flowing and standing aerated water. The first type of hydrodynamic perturbations was created by a streamlined obstacle at the tank bottom; the second one - by rotating propellers. Two sorts of statistical amplitude distribution of red laser light scattering in a near-water aerosol located above the perturbation region are established. It is established that various statistical distributions of the amplitudes of the laser radiation scattering pulses on the particles of the near-water aerosol and, accordingly, the different aerosol distributions in size, correspond to these various hydrodynamic perturbations. Normalized amplitude distribution histograms of light scattering are compared.

Here we report on a comparative analysis of laser techniques for detection and speciation of radionuclides and its complexes in the geosphere. The application of different methods is illustrated by the example of uranium(VI) speciation in aqueous environment and detection of trace elements on the ppm level in gases, which appear as a result of reprocessing of spent nuclear fuel.

The algorithm for estimation of the quantum yield of phytoplankton fluorescence from the remote sensing satellite of the MODIS tool is discussed in the paper. There is an example of manifestation of the iron limitation in the Amundsen Sea. Amundsen Sea encloses two polynyas: Fe-limited ASP (Amundsen Sea Polynya) and Fe-replete PIP (Pine Island Polynya). We present a procedure for comparing the mean values of the quantum yield of phytoplankton fluorescence in these regions and the requirements for it. To meet these requirements, the data of two satellite systems were analyzed and compared: MODIS and AVHRR. Analysis of the data made it possible to observe the differences in the mean values of the quantum yield of phytoplankton fluorescence in these two regions during the bloom period of the Amundsen Sea phytoplankton in 2012.

The problem of exact mathematical models of potential surface waves propagation is considered. The existing models converting the original system of hydrodynamic equations and boundary conditions into some new form are analyzed. A new approach to the above mentioned problem is presented resulting in the single equation for the waveform. The relations permitting to reconstruct all physical fields on the base of this waveform are formulated. It is shown how on the base of the equation received to construct all well-known results of approximate theories of stationary surface waves.

In this work, the waves and currents generated by prognostic wind in the Sea of Azov are investigated using a three-dimensional nonlinear sigma-coordinate Princeton Ocean Model. The mathematical model was also used for studying the transformation of passive admixture in the Sea of Azov, caused by the spatiotemporal variations in the fields of wind and atmospheric pressure, obtained from the prediction SKIRON model. Comparison of the results of numerical calculations and the data of field observations, obtained during the action of the wind on a number of hydrological stations was carried out. The growth of storm surges, velocities of currents and the characteristics of the pollution region at different levels of intensity of prognostic wind and stationary currents were found. The obtained results are presented in the table of the sea level changes caused by the onshore and offshore winds and the current velocities for different characteristics of constant and variable wind. The results of a comprehensive study allow reliably estimate modern eco-logical condition of offshore zones, develop predictive models of catastrophic water events and make science-based solutions to minimize the possible damage.

The problem of computation of vertical temperature distribution in inland water objects is raised in the research, and the modified version of the program complex LAKE is proposed for its solving. Also the results of validation of the modified version in accordance with the parameters of lake part of Gorky water reservoir are provided. The modification caused changing the procedure of input data assignment, ensured the possibility of using the results from field measurements as starting profiles, led to the greater consideration of wind influence on mixing and allowed to reproduce general forms of distribution more accurately. The data from the experimental sites of Gorky water reservoir in combination with the files of global reanalysis and the data of hydrometeorological station were used for validation. Measurements of the vertical temperature profiles were carried out with freely sinking CTD-probe, which recorded the temperature values several times per second. Time and temperature dependences in control points, comparison of the forms of the profiles and standard deviation were analyzed to assess the results of numerical modeling. Numerical simulation with the modified model gave results which were in good agreement with the real seasonal variations of thermal regime in lake part of Gorky water reservoir. The best quantitative and qualitative agreement was obtained for the thermal regimes with strong mixing: the results of the forecasting reproduced the forms of distribution and the values of temperature extremely accurately. The results for the ones with strong stratification demonstrated less accuracy in the values of temperature in control points, particularly near the surface, but all specificities of the forms of vertical temperature distribution were correctly reproduced.

The paper presents the results of the investigation of the strain-strength properties of rocks (dolomites) raised from a depth of more than 6 km of the exploration well of the Kainsayskaya Field. The experiments were carried out on a unique experimental setup – the Triaxial Independent Load Test System of IPMech RAS on cubic specimens with an edge of 40 mm. Two triaxial tests were performed on two specimens showing the presence of strong strength anisotropy of the rock. A physical simulation of the pressure reduction process in deep wells near an open borehole and the tip of a perforation hole was performed on three specimens. The conducted studies have revealed a rather low strength of the studied rocks, despite the great depths of their lying under the conditions of high rock pressure. They have shown that the beginning of the rock destruction depends vastly on the type of stress state arising in the formation. Carrying out physical modeling of geomechanical processes in oil and gas reservoirs using true triaxial loading is of great importance from the point of view of justifying methods of influence on deep-lying strata in order to increase the productivity of wells, as well as reduce risks of well destruction during their drilling and operation.

The approach to modeling geomechanical processes in the well vicinity including mathematical modelling of deformation, fracture and filtration as well as experimental determining the parameters involved, under conditions, corresponding to the real in situ ones is presented. The approach involves three stages: (i) choosing the mechanical model and its adopting to the considered problem; (ii) determining the model parameters by using the direct experiments; (iii) mathematical modeling of deformation, fracture and filtration processes in question.The important mechanical model feature is that it accounts for anisotropy of mechanical and filtration properties and dependence of yield transition on volumetric stresses and pore pressure. Another important peculiarity consists in using the experimentally determined dependences of permeability on stress-strain state.The results of the experimental determination of the model parameters for two lithotypes of Kirinsky field and one lithotype of Filanovsky field using the Triaxial Independent Loading Test System (TILTS) are given. Numerical simulation for the used model for the cases of uncased and perforated bottomhole is presented. The stress concentrations and production rate are calculated. The results of the work carried out demonstrate the capability of the approach to solve geomechanical problems in order to optimize technological processes.

The movement of a large satellite around a model planet, which is a thick spherical layer of a heavy, perfect liquid with a solid nucleus, is being discussed. The tidal disturbance caused by the satellite is propagated by long gravity waves. When the satellite is gliding along the layer surface the energy and orbital period decrease, and the tidal height and period of free gravity waves supporting the tide growth increase. To maintain the tide the orbital period should not be less than the period of free long gravity waves. The value of static tide is assessed for the case when orbital period and free gravity waves expending over the surface of spherical liquid layer periods coincide. When this condition is met gliding becomes impossible and the satellite fully submerges. With regard to the Earth, movement of the satellite projection is supersonic for the material composing the mantle above a certain horizon, and subsonic for underlaying horizons. The pressure of the tide bulge has effect on the entire lower layer and on a narrow front area of shock wave in the upper layer. Therefore, a considerable horizontal stress occurs at the abovementioned horizon. When the stress exceeds the shear strength limit, the upper layer of the mantle starts to move at a finite velocity in relation to the lower mantle. A melt forms in the friction layer, so the velocity of longitudinal seismic waves decreases. The boundary of supersonic and subsonic velocities gradually lowers increasing the melt layer thickness and forming an abrupt jump in seismic wave velocities. After the boundary reaches the horizon at 220 km, the satellite submerges into the mantle. This is the reason why at present moment, after the melt solidification there is a low velocity zone of seismic waves in the upper mantle and a 220 km seismic boundary.

On the basis of numerical experiments with the ocean model INMOM adapted for the Baltic Sea conditions, the influence of baroclinic processes on sea level oscillations is investigated. It is shown that baroclinic perturbations make a significant contribution to the total Baltic Sea level oscillations. Baroclinic effects have the dominate impact on formation of the mean sea level. The spectral analysis testifies the most considerable contribution of baroclinic fluctuations in the ranges of seasonal and mesoscale variability. The highest amplitudes of sea level baroclinic perturbations are noted in eastern part of the Gulf of Finland where they reach +30 cm, as well as in Bay of Bothnia and Gulf of Riga (+20 ÷ 25 cm). The greatest intensity of the baroclinic sea level oscillations is noted during the autumn and winter period in the local regions of open Baltic, the Bay of Bothnia, eastern part of the Gulf of Finland, Gulf of Riga, as well as the Kattegat and the Danish Straits.